Made an account just to post a workaround on this since it was annoying me too.
It seems like the Client Loader is invalidating some data in a few of the pak files, then they have to be (re)updated again after clicking Login. It is only about 50MB of data before the game screen pops up, but there is actually even more downloading that continues in the background for quite a while. People with plenty of bandwidth probably hardly notice the login delay, but either way it's a waste of bandwidth.
What I've been doing to avoid this is bypassing the client loader. All it takes is a shortcut or batch file that calls Entropia.exe directly with the proper parameters. It was actually popular years ago for fast logins (with our passwords in cleartext!)
Example entropia.bat:
F:\Games\Entropia\bin64\Entropia.exe --run -disable_streaming_audio -windowmode
Use the batch file or new shortcut to launch Entropia instead of the Client Loader. The first time it will still do the slow login (unless you happened to close Client Loader before last exit) but subsequent logins should be fast. You'd want to delete the shortcut after MA fixes the issue, of course.
Btw, another option would be to just make a copy of the few pak files that change (shared_item_01.pak, shared_platform, etc). Start Client Loader, Launch the login screen (but don't login yet), then close the client loader, copy the good files back, then login.